Find the next number in the sequence 47, 43, 40, 38, 37, 33, ..

Answer:

Let's represent Adeline's age now as A.

i. Adeline's age in 10 years' time can be expressed as A + 10.

ii. Adeline's age 6 years ago can be expressed as A - 6.

So, we can write an equation for A as follows:

A + 10 = A - 6

Solving for A, we can simplify the equation as follows:

16 = A - 6

Adding 6 to both sides, we get:

22 = A

Therefore, Adeline's age now is 22 years old.

Both (7) and (8) are true, which means that the ordered pair (1,-6) satisfies both of the inequalities (1) and (2). Hence, (1,-6) is a solution of the given system of inequalities.

To determine if a given ordered pair is a solution of the system of inequalities:

2x - y > -5 (1)

y ≤ -3x - 3 (2)

We need to substitute the values of x and y into the inequalities and check if they satisfy both of them simultaneously.

Let's say we have an ordered pair (a,b), then we need to check if:

2a - b > -5 (3)

b ≤ -3a - 3 (4)

If (a,b) satisfies both inequalities (3) and (4), then it is a solution of the given system of inequalities.

Let's consider an example ordered pair (1,-6) and check if it is a solution of the system of inequalities:

Substituting the values of x=1 and y=-6 into the inequalities (1) and (2), we get:

2(1) - (-6) > -5 (5)

-6 ≤ -3(1) - 3 (6)

Simplifying (5) and (6), we get:

8 > -5 (7)

-6 ≤ -6 (8)

Both (7) and (8) are true, which means that the ordered pair (1,-6) satisfies both of the inequalities (1) and (2). Hence, (1,-6) is a solution of the given system of inequalities.

for such more question on inequalities.

https://brainly.com/question/17448505

#SPJ11

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

Answer:

Step-by-step explanation:

\(\frac{4}{5}+\frac{3}{20}\\ \\ \frac{4}{5}\left(\frac{4}{4}\right)+\frac{3}{20}\\ \\ \frac{16+3}{20}\\ \\ \frac{19}{20}\)

A) An estimate can be (1.5, 2.5)

B) the system of equations is:

y = x + 1

y = -2x + 5

C) The real solution is (4/3, 13/3)

The solution of the system of equations is the point where the graphs intercept. Here we can see that the intercept is at something like (1.5, 2.5)

b) A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

The first line cross the y-axis at y = 1

y = a*x + 1

And also passes through (-3, -2), replacing these values:

-2 = a*-3 + 1

-2 -1 = a*-3

-3 = a*-3

-3/-3 = 1 = a

this line is y = x + 1

The other line passes through the y-axis at y = 5

y = a*x + 5

And also passes through (1, 3), then:

3 = a*1 + 5

3 - 5= a*1

-2 = a

y = -2x + 5

Then the system of equation is:

y = x + 1

y = -2x + 5

The solution is at:

x + 1 = -2x + 5

x + 2x = 5 - 1

3x = 4

x = 4/3

And the value of y is:

y = 4/3 + 1 = 13/3

Then the actual solution is (4/3, 13/3)

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

Three lots with parallel side boundaries extend from the avenue to the boulevard.

x + y + z = 140 meters

According to the proportion theorem,

Solving for x, using cross multiplication:

Similarly,

x/40 = z/35

solving for z by cross multiplication,

z = 35x/40

z = 7x/8

Now, the third proportions,

y/30 = z/35

Solving for y,

y = 30z/35

y = 6z/7

x + y + z = 140

4y/3 + 6z/7 +  7x/8 = 140

(224y + 144z + 147x)/168 = 140

224y + 144z + 147x = 23520

Substituting z = 7x/8,

224y + (144 × 7x/8) + 147x = 23520

224y + 126x + 147x = 23520

224y + 273x = 23520

Now,

Substitute y = 3x/4

(224×3x/4) + 273x = 23520

168x + 273x = 23520

441x = 23520

x = 53.33

Now,

We know that

y = 3x/4

so,

y = 40

And,

z = 7x/8

Z = 46.66

To learn more about parallel here:

https://brainly.com/question/16701300

#SPJ4

Answer:

Step-by-step explanation:

The equation of the sphere that passes through the point (5, 8, 3) and has center (8, 1, -5) is (x - 8)² + (y - 1)² + (z + 5)² = 122.

To find the equation of a sphere that passes through the point (5, 8, 3) and has a center at (8, 1, -5), we can use the standard form equation of a sphere:

(x - h)² + (y - k)² + (z - l)² = r²,

where (h, k, l) represents the center of the sphere, and r represents the radius.

Given that the center is (8, 1, -5), we can substitute these values into the equation:

(x - 8)² + (y - 1)² + (z + 5)² = r².

Now, we need to find the radius, which is the distance between the center (8, 1, -5) and the point (5, 8, 3).

We can use the distance formula:

r = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²],

where (x₁, y₁, z₁) represents the center and (x₂, y₂, z₂) represents the given point.

Substituting the values, we get:

r = √[(5 - 8)² + (8 - 1)² + (3 - (-5))²]

= √[(-3)² + 7² + 8²]

= √[9 + 49 + 64]

= √[122]

= √122.

Now we can write the equation of the sphere:

(x - 8)² + (y - 1)² + (z + 5)² = (√122)²

(x - 8)² + (y - 1)² + (z + 5)² = 122.

For similar question on sphere.

https://brainly.com/question/30522100

#SPJ8

Answer:

orientation is preserved (stays the same)

Step-by-step explanation:

The probability of selecting chocolate of the first type at random is 1/3.

Since there are three types of chocolates with 6 pieces each, there are a total of 18 chocolates in the box.

The probability of selecting chocolate of the first type is the number of chocolates of the first type divided by the total number of chocolates in the box.

Since there are 6 chocolates of the first type, the probability of selecting a chocolate of the first type is:

Probability = (Number of chocolates of the first type) / (Total number of chocolates)

= 6 / 18

= 1/3

Therefore, the probability of selecting chocolate of the first type at random is 1/3.

To learn more about probability visit: https://brainly.com/question/30034780

#SPJ11

Answer:

the real answer is (8,-4)

Step-by-step explanation:

If the midpoint of the AB is (5.5, 0) then the coordinate of the B will be given as (8, -4).

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

Point A is at (3, 4) and point M is at (5.5,0).

Point M is the midpoint of points A and B.

Then the point of B is given as

\(\rm (x_1,y_1) = (2x-x_2, 2y-y_2)\\\\(x_1,y_1) = (2\times 5.5 - 3, 2\times 0-4)\\\\(x_1,y_1) = (8, -4)\)

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567

The least accurate measurement among the options provided is 18050 m.Therefore, among the given options, 18050 m is the least accurate measurement due to its higher number of significant figures.

To determine the least accurate measurement, we need to consider the number of significant figures in each measurement. The measurement with the fewest significant figures indicates lower accuracy.

Among the options given:

a. 208 m has three significant figures.

b. 18050 m has five significant figures.

c. 0.08 m has two significant figures.

d. 0.750 m has three significant figures.

e. 12.0 m has three significant figures.

The measurement with the least accurate value is 18050 m because it has the highest number of significant figures among the options. A higher number of significant figures suggests a greater level of precision and accuracy in the measurement.

Significant figures represent the digits in a number that contribute to its precision. They include all the non-zero digits and any zeros that appear between non-zero digits or after a decimal point. In this case, the measurement 18050 m has five significant figures, indicating a high level of precision and accuracy.

On the other hand, measurements with fewer significant figures imply less precision and accuracy. For example, the measurement 0.08 m has only two significant figures, suggesting less certainty in the measurement compared to 18050 m.

To learn more about Significant figures : brainly.com/question/29153641

#SPJ11

Answer:

x= -3

Step-by-step explanation:

you replace y with -2 as the output

then subtract the 7 on both sides to have '-9=3x'

divide by 3 on both sides

x= -3

Answer:

x=-3

Step-by-step explanation:

y=3(-3)+7

y=-9+7

y=-2

Answer:

absolute value of n - 29

Step-by-step explanation:

n - 29

Answer:

1738 kilometers

Step-by-step explanation:

Answer:

120 total interest

Step-by-step explanation:

1500 x 0.02 =30 30 x 4 = 120

Answer:

3,804.80

Step-by-step explanation:

10% criterion The sample size must be less than 10% of such population size in order to utilize a binomial distribution for approximate the number of successes in a srs since the sample size is significantly too tiny when related to the population.

For the given question-

Thus, this means that, in this case, its sample size n must represent less than 10% of a population size N.

To know more about the binomial distribution, here

https://brainly.com/question/15557838

#SPJ4

Answer:

  (a) 56

Step-by-step explanation:

You want the number that is 80% of 70.

In this context, "of" means "times." Thus "80% of 70" is "80% times 70".

Some calculators have a % key that lets you calculate this directly. Otherwise you may need to convert the percentage to a fraction.

The % symbol is effectively interchangeable with "/100", so we have ...

  80% of 70 = 80/100 × 70

At this point, you can employ what you know about multiplication and division to simplify this to a problem you can do in your head.

  = (80×70)/100 = (8×7×100)/100 = 8×7 = 56

If you want a grade of 80%, you need to get 56 questions correct.

Answer:

17

Step-by-step explanation:

17 - 12 is 5.

Answer:

C

Step-by-step explanation:

negative four raised to the sixth power divided by negative four raised to the fourth power

because  negative four raised to the fourth power divided by negative four raised to the second power = negative four raised to the second power

negative four raised to the sixth power divided by negative four raised to the fourth power also = negative four raised to the second power

The answer is A: negative four raised to the second power divided by negative four raised to the fourth power. This is obtained by applying the rules of exponents, specifically, when dividing with the same base, subtract the exponents.

This question pertains to exponents division rules. According to the rule of Power of a Power in exponents, when you divide expressions with the same base, you subtract the exponents. So if you have negative four raised to the fourth power (-4⁴) and you want to divide it by negative four raised to the second power (-4²), you subtract 2 from 4 to get an exponent of 2. This results in a negative four raised to the second power (-4²). So, the correct option from the given choices in your question is A: negative four raised to the second power divided by negative four raised to the fourth power.

Learn more about Exponents here:

https://brainly.com/question/5497425

#SPJ2

one leg of a right triangle is 6 inches longer than the other leg, and the hypotenuse is 30 inches. Thus,

The lengths of the legs of the triangle are 18 inches,24 inches and  30 inches.

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Given that,

one leg of a right triangle is 6 inches longer than the other leg.

hypotenuse is 30 inches.

Let assume, the other leg be x

It is given that, one leg of a right triangle is 6 inches longer than the other leg. So, One leg = x + 6

Since it is a right angled triangle,

h² = p² + b²

Where, h = hypotenuse

p = perpendicular

B = Base

So, (30)² = (x+6)² + x²

or, x = -24, 18

As, the length of side cannot be negative so x becomes 18.

Thus, x + 6 = 18 + 6 = 24 inches

Hypotenuse = 30 inches

Hence, the lengths of the legs of the triangle are 18 inches, 24 inches and  30 inches.

To know more about right triangle refer to:

https://brainly.com/question/29869536

#SPJ4

Answer: D. f(x)-2

Step-by-step explanation:

Changes insides the parenthesis translate left and right. If it is [+] a number, then it is moving to the left. If it is [-] a number, then it is moving to the right.

Changes outside the parenthesis translate up and down. If it is [+] a number, then it is moving upward. If it is [-] a number, then it is moving downward.

----------------------------------------------------------------------------------------------------

Given

Translate f(x) 2 units downward

Solve

According to the rules, it should be -2 units outside of the parenthesis

Therefore, it should be f(x)-2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

D. f(x) – 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

(4,4)

-9 in the y-axis

(4,-5)

-1 in the x-axis

(3,-5)

Answer:

X=11

Step-by-step explanation:

Vertical angles equal each other.

5x+10 = 7x -12

Then solve for x by placing all the X values on one side and the number values on the other side.

5x+10=7x-12

5x-7x=-12-10

-2x=-22

x=11

Answer:

Option D. 10,779 feet

Step-by-step explanation:

Given from the figure attached,

PT = OB = 7000 ft

PB = OT = x feet

and angle of elevation (∠POT) = 30°

By applying Tan rule in the triangle POT,

tan33° = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\) = \(\frac{PT}{OT}\)

tan33° = \(\frac{7000}{x}\)

x = \(\frac{7000}{\text{tan}33}\)

x = 10779 feet

Therefore, distance between the bird (B) and plane (P) is 10,779 feet.

Option D. will be the answer.

Answer:

10,779 feet

Step-by-step explanation:

I took the test.

The area of kite ABCD is equal to half the product of the sum of its diagonals and the height between them.

Since kite ABCD is divided into two triangles by its diagonals, we can find the area of the kite by finding the sum of the areas of these two triangles.

Let AC and BD be the diagonals of the kite, intersecting at point E. Then triangle ABE and triangle CDE are the two triangles formed by the diagonals.

The area of a triangle can be found using the formula: Area = (base x height) / 2

For triangle ABE, the base is AB and the height is the distance from E to the line containing AB. Similarly, for triangle CDE, the base is CD and the height is the distance from E to the line containing CD.

Since the diagonals of a kite are perpendicular and bisect each other, the distance from E to the line containing AB is the same as the distance from E to the line containing CD.

Therefore, the heights of the two triangles are equal.

So, we can find the area of ABCD as follows:

Area of ABCD = Area of triangle ABE + Area of triangle CDE

= (AB x height)/2 + (CD x height)/2

= (AB + CD) x height / 2

Therefore, the area of kite ABCD is equal to half the product of the sum of its diagonals and the height between them.

Learn more about area of the kite

brainly.com/question/15640807

#SPJ11

Answer:

Step-by-step explanation:

This is kinda tricky, but not nearly as bad as d = rt problems. Those are a nightmare!

We will make a table for this:

                         #lbs solution           *          % salt         =           lbs. salt

  3% solution

-  Water                                                                                                      

New solution

And we will now fill in what we know. The 3% solution part is easy. The number of pounds of that is 50 and the percent salt in 3% salt is....well, 3%. As a decimal, it is .03:

                             #lbs solution        *        %salt        =        lbs salt

  3% solution                50                 *          .03         =           1.5

-  Water                                                                                                

New solution

The last column there with a 1.5 in it is the product of 50 times .03, since that is what the formula at the top of the table tells us we have to use. Now for the water. That's easy, too, since the amount of water we are evaporating (notice the subtraction sign out front of the word "water"; that indicates we are removing water) is our unknown, and we also know that water has 0% salt in it:

                          #lbs solution         *       %salt        =        lbs. salt

   3% solution            50                  *         .03         =           1.5

-   Water                       x                  *            0          =            0        

New solution

Now all we have left is the new solution row and the equation. Finding the equation from a mixture table is as easy as it can be! Super easy!

The new solution will be 50 - x since, going down column 1, we are subtracting the water from the 3% solution, the % salt is to be 5%:

                            #lbs. solution        *       %salt        =        lbs. salt

   3% solution               50                *         .03          =           1.5

-   Water                          x                 *           0           =            0        

New solution         50 - x                  *         .05          =     2.5 - .05x

Now we're ready for our equation. I got the 2.5 - .05x from multiplying

.05(50 - x), just so you know.

if we had to subtract the water from the salt solution and set it equal to the new solution in the first column, we also have to do it in the third column:

1.5 - 0 = 2.5 - .05x and solve for x:

-1 = -.05x so

x = 20 pounds of water

Answer:

Black! I like black beacuse it reminds me of my dad!

Step-by-step explanation:

Answer: 15 months

Step-by-step explanation: